SODOS is Sum Of Defeated Opponents' Scores.
It is defined as the Sum of Defeated opponent's McMahon scores,
As the name SODOS suggests, its value depends upon how many opponents you have defeated. If you lose all your games then your SODOS is zero. If you beat two others then it is the sum of two scores. If you beat 10 others then it is the sum of 10 scores.
The intent behind using it is to discover how strong your opponents were. The theory being that if you have defeated a stronger set of opponents than another player on the same final score, then you are slightly stronger / better than they are.
SODOS is also sometimes abbreviated as SDOS.
It is sometimes used in round robin tournaments, where SOS is of no use. However it still suffers as described below.
SODOS differences are NOT always invariant under change of origin of the McMahon Pairing scale.
The origin of the McMahon Pairing scale does vary: it is zero at 20 kyu in many European tournaments, it is zero at shodan in the UK.
Here is an example of a 3 round tournament illustrating concerns about using SoDoS as a tie breaker.
We have a shodan Alan winning 2 games playing:
Bob(1k)-, Cath(1d)+ Dave(1k)+
We have a 1kyu Juliet winning 3 games playing:
Karen(1d)+ Lionel(1k)+ Martin(1k)+
It is not necessary to show the entire tournament results table. Here is a summary of the key information for Alan's and Juliet's opponents' scores in UK and EU styles.
Alan's opponents:
UK MMS Euro MMS Name Wins initial final initial final Bob(1k) 2 -1 1 19 21 Cath(1d) 1 0 1 20 21 Dave(1k) 2 -1 1 19 21
Juliet's opponents:
UK MMS Euro MMS Name Wins initial final initial final Karen(1d) 0 0 0 20 20 Lionel(1k) 2 -1 1 19 21 Martin(1k) 2 -1 1 19 21
If we use SoDoS as the one and only tie breaker, then we can construct the portion of the final ranklist showing both Alan's and Juliet's position. The column MMSi is the initial McMahon Pairing score, and MMSf is the final McMahon Pairing score.
Using the UK scale, we have Alan and Juliet ranked equal and sharing any prize:
Wins MMSi MMSf SoDoS WHO CONTRIBUTES TO SODOS Juliet(1k) 3 -1 2 0+1+1=2 Karen+Lionel+Martin Alan(1d) 2 0 2 1+1=2 Cath+Dave
Using the EU scale Juliet is ahead of Alan, Juliet gets the prize:
Wins MMSi MMSf SoDoS WHO CONTRIBUTES TO SODOS Juliet(1k) 3 19 22 20+21+21=62 Karen+Lionel+Martin Alan(1d) 2 20 22 21+21=42 Cath+Dave
It does not matter here which result is better. It demonstrates that SODOS is flawed and should not be used.
Note that if you use SOS (Sum of all opponents McMahon scores) as the tie breaker, then this effect does not happen because you are summing over all games, not just a selection.
Read the example above again comparing either scheme with one where a shodan scores -100. In that case a player with no wins scores 0 whilst one with several wins will be far worse off with a score of minus several hundred!
This page was WMEd by SGBailey on 2004-12-18. The entire old contents of the page was appended to the discussion page. Original input from me, Geoff Kaniuk, Matti, barry, Christopher Gerlach, Jens Baaran, DrStraw, wms.